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Cost-Volume-Profit Analysis

This chapter focuses on understanding how changes in volume affect costs, including the behavior of variable, fixed, and mixed costs. It also covers the high-low method, relevant range, breakeven point, contribution margin, and profit planning using CVP analysis.

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Cost-Volume-Profit Analysis

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  1. Cost-Volume-Profit Analysis Chapter 21

  2. Objective 1 Identify how changes in volume affect costs

  3. Cost Behavior • How costs change in response to changes in a cost driver • Cost driver - any factor whose change makes a difference in a related total cost • Volume (units or dollars) - most prominent cost driver in cost-volume-profit (CVP) analysis

  4. Cost Behavior • Variable costs - change directly in proportion to changes in volume • Fixed costs - remain constant (fixed) for a given time period despite fluctuations in volume • Mixed costs - have both fixed and variable components

  5. Assume we pay sales commissions of 5% on all sales. The cost of sales commissions increase proportionately with increases in sales Total Variable Costs

  6. Variable Cost Per Unit • Variable costs per unit do not changeas activity increases In the previous example, sales persons get $.05 for every dollar of sales. If a sales person has sales of $1,000 or $15,000, she gets $.05 for every dollar

  7. Total Fixed Costs Assume we pay our sales staff a salary of $2,000 per month. If a sales person makes sales of $500, she gets paid $2,000 salary. If she has sales of $100,000, she gets paid $2,000 salary

  8. Mixed Costs A mixed cost has elements of both fixed and variable costs. Assume we pay our sales staff, $2,000 plus 5% commission on each sales dollar

  9. Mixed Costs Variable Fixed

  10. E21-14 _____ 1. Oil filter _____ 2. Building rent _____ 3. Oil _____ 4. Wages of maintenance worker _____ 5. Television _____ 6. Manager’s salary _____ 7. Cash register _____ 8. Equipment V F V V F F F F

  11. E21-15 a

  12. E21-15 b

  13. E21-15 c

  14. High-Low Method • Method to separate mixed costs into variable and fixed components • Select the highest level and the lowest level of activity over a period of time In order to do CVP analysis, we have to classify costs as to whether they are fixed or variable. One method of doing this is the high-low method

  15. High-Low Method – E21-16 Step 1: Calculate variable cost/unit = Δ total cost / Δ volume of activity ($4,000-$3,600) ÷ (1,000-600) $400 ÷ 400 = $1

  16. High-Low Method - E21-16 Step 2: Calculate total fixed costs = Total mixed cost – Total variable cost $4,000 – ($1 * 1,000) = $3,000 or $3,600 – ($1 * 600) = $3,000

  17. High-Low Method – E21-16 Step 3: Create and use an equation to show the behavior of a mixed cost Total mixed cost = $1x + $3,000 = ($1 * 900) + $3,000 = $3,900

  18. Relevant Range • Band of volume: Where total fixed costs remain constant and variable cost per unit remains constant • Outside the relevant range, the cost either increases or decreases CVP analysis is only valid within a relevant range, which is usually the range that could reasonably be expected for our business

  19. Objective 2 Use CVP analysis to compute breakeven point

  20. Assumptions • Expenses can be classified as either variable or fixed • The only factor that affects costs is change in volume

  21. Breakeven Point • Sales level at which operating income is zero • Sales above breakeven result in a profit • Sales below breakeven result in a loss

  22. Income Statement Approach This income statement classifies expenses according to behavior Contribution margin is the excess of sales revenue over variable costs that contributes to covering fixed costs and then to providing operating income Contribution Margin Income Statement Sales - Variable Costs Contribution Margin - Fixed Costs Operating Income To compute breakeven point set the equation equal to zero

  23. Contribution Margin Approach Breakeven units sold = Fixed costs + Operating income Contribution margin per unit

  24. Contribution Margin Ratio Contribution margin ÷ Sales revenue Breakeven sales dollars = Fixed costs + Operating income Contribution margin ratio

  25. E21-17 1. Contribution margin ÷ Sales revenue $187,500 ÷ $312,500 = 60%

  26. E21-17 2. Aussie Travel Contribution Margin Income Statement Three Months Ended March 31, 2007 Sales revenue $250,000 $360,000 Variable Costs (40%) (100,000)(144,000) Contribution Margin (60%) $150,000 $216,000 Fixed Costs (170,000)(170,000) Operating Income $(20,000) $46,000

  27. E21-17 2. Breakeven sales dollars = Fixed costs + Operating income Contribution margin ratio $170,000 + $0 .60 $283,333

  28. E21-18 1. Contribution margin = Sales–Variable costs = $1.70 - $0.85 = $0.85 2. Breakeven units sold = Fixed costs + Operating income Contribution margin per unit ($85,000 + $0) / $0.85 = 100,000 units 100,000 units x $1.70 = $170,000

  29. Objective 3 Use CVP analysis for profit planning and graph relations

  30. Plan Profits Use the same techniques used for breakeven point Example: The following information is available for Conte Company. Sale price per unit $30 Variable costs per unit 21 Total fixed costs $180,000 Target operating income $90,000 How many units must be sold to meet the targeted operating income?

  31. Plan Profits Sales – variable costs – fixed costs = operating income $30x – $21x - $180,000 = $90,000 $9x = $270,000 x = 30,000 units

  32. Preparing a CVP Chart Step 1: • Choose a sales volume • Plot point for total sales revenue • Draw sales revenue line from origin

  33. Preparing a CVP Chart •

  34. Preparing a CVP Chart Step 2: Draw the fixed cost line

  35. Preparing a CVP Chart

  36. Preparing a CVP Chart Step 3: Draw the total cost line ( fixed plus variable)

  37. Preparing a CVP Chart

  38. Preparing a CVP Chart Step 4: Identify the breakeven point and the areas of operating income and loss

  39. Preparing a CVP Chart Breakeven point Profit Loss

  40. Profit E21-21 Breakeven point Total Costs Fixed Costs Revenues

  41. Objective 4 Use CVP methods to perform sensitivity analysis

  42. Sensitivity Analysis • “What if” analysis • What if the sales price changes? • What if costs change?

  43. E21-22 Sale price per student $200 Variable costs per student 120 Total fixed costs $50,000 1. Contribution margin per unit: $200 – 120 = $80 Breakeven point: $50,000 ÷ $80 = 625 students

  44. E21-22 Sale price per student $180 Variable costs per student 120 Total fixed costs $50,000 2. Contribution margin per unit: $180 – 120 = $60 Breakeven point: $50,000 ÷ $60 = 833 students

  45. E21-22 Sale price per student $200 Variable costs per student 110 Total fixed costs $50,000 2. Contribution margin per unit: $200 – 110 = $90 Breakeven point: $50,000 ÷ $90 = 556 students

  46. E21-22 Sale price per student $200 Variable costs per student 120 Total fixed costs $40,000 1. Contribution margin per unit: $200 – 120 = $80 Breakeven point: $40,000 ÷ $80 = 500 students

  47. Margin of Safety • Excess of expected sales over breakeven sales • Drop in sales that the company can absorb before incurring a loss

  48. E21-23 Margin of safety = Expected sales – breakeven sales Expected sales: Sales – variable costs – fixed costs = operating income 1x - .70x - $9,000 = $12,000 .30x = $21,000 x = $70,000

  49. E21-23 Margin of safety = Expected sales – breakeven sales Breakeven sales: Sales – variable costs – fixed costs = operating income 1x - .70x - $9,000 = $0 .30x = $9,000 x = $30,000

  50. E21-23 Margin of safety = Expected sales – breakeven sales = $70,000 - $30,000 = $40,000

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